one would assume whatever deal this is doesn’t allow for a lot of prep time or extra money.

Why would we assume that? We assume that you become immortal, and are sent back in time, and the part that seems unrealistic to you is that you’d prepare for the trip before you go? :P

Any money that existed then would exist today, so you avoid anything serialized. Stick to things that are non-serialized and fungible- precious metals for example, or gemstones (without laser serial #s of course). Pre-serial cash would work too (probably the easiest to counterfeit in modern times).

But as for existence paradox-- the mere action of going back would create such an issue if it is an issue. All the molecules in your body and clothes existed in 1945, if perhaps in different arrangements-- IE anything plastic might have been in the ground as crude oil, the molecules of your body would be things like plants, dirt, trees, etc, anything metal you have would be ore in the ground, etc. And per butterfly effect paradox, from the instant you arrive you’ve changed things, just by breathing and walking around you’ve affected air flows and converted a little more oxygen to CO2. If you arrive in the middle of nowhere, hold still for 30 seconds, then depart again, that might have no real effect. Or it might create a butterfly effect that changes a weather pattern or something and has a huge effect.

By that measure, the whole thing becomes a not fun exercise in paranoia- knowing that even saying hello to someone (or not saying hello) might alter the future and erase your existence.